{
  "id": "1903.01980",
  "version": "v1",
  "published": "2019-03-05T18:49:40.000Z",
  "updated": "2019-03-05T18:49:40.000Z",
  "title": "Statistical Guarantees for the Robustness of Bayesian Neural Networks",
  "authors": [
    "Luca Cardelli",
    "Marta Kwiatkowska",
    "Luca Laurenti",
    "Nicola Paoletti",
    "Andrea Patane",
    "Matthew Wicker"
  ],
  "comment": "9 pages, 6 figures",
  "categories": [
    "cs.LG",
    "cs.CV",
    "stat.ML"
  ],
  "abstract": "We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i.e., with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-05T18:49:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bayesian neural networks",
      "statistical guarantees",
      "approximate bnn inference techniques",
      "image classification tasks",
      "estimate probabilistic robustness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}